**Question**: You have 120 meters of string that you use to make a square that has an area of 900 square meters. You want to use the 120 meters of string to create a rectangle that is only 500 square meters? What are the dimensions of the rectangle?

**Answer**: The square made with 120 meters of string has four sides of 30 meters each. (30 x 4 =120 and 30 x 30= 900).

This is a classic quadratic equation problem. We add some string to make the length longer
and subtract the same amount of string to make the width shorter

A=(X+K) x (X-K) = X

^{2}– K^{2}
We know that 900-400 is equal to 500 so k is the square root
of 400 or 20. The dimensions of the
rectangle are length of 50 and width of 10.
The sum of the sides of the rectangle 50+50+10+10 is 120.

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